Since September 12, the two sides have held seven contact group meetings, but could not agree on two disputed points, TOLO News said in a report.
And for the last six days, there has not been any contact group meetings either.
Amid the delay in the talks, diplomatic efforts by Afghanistan's allies have started as US special envoy Zalmay Khalilzad was in Doha last week and met with negotiating teams of the two sides.
Meanwhile, NATO's Senior Civilian Representative, Stefano Pontecorvo, also held talks with chief negotiator Masoom Stanekzai and discussed the peace process.
This development also comes as Abdullah Abdullah, chairman of the High Council for National Reconciliation, will visit India on October 6, his spokesman Fraidoon Khwazoon confirmed.
"The aim of the trip is to attract support for the Afghan peace and strengthen regional consensus.
Abdullah Abdullah will meet with Indian officials on Afghan peace and bilateral relations between Afghanistan and India," TOLO News quoted Khwazoon as saying.
Last week, Abdullah also visited Pakistan and discussed the Afghan peace process with Prime Minister Imran Khan, Foreign Minister Shah Mahmood Qureshi, and other senior officials.
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